Chapter02TimeValueofMoney

Chapter02TimeValueofMoney - OEM 2009 Program Time Value of...

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OEM 2009 Program Time Value of Money Page 1 CHAPTER 2 Time Value of Money Time Value of Money Definitions : PV = Present value FV = Future vale i = Interest rate i = Compounding rate i = Discount rate N = Number of time periods Time Value of Money PMT = Annuity or perpetuity payment CF t = Cash flow (period t) FVIF i,N Interest factors PVIF i,N for single values FVIFA i,N Interest factors PVIFA i,N for regular annuities Future Value - Single Cash Flow FV N = [PV] [(1 + i) N ] FV N = [PV] [FVIF i,N ] FVIF i,N = (1 + i) N 1,000.00 1,120.00 1 Deposit at t = 0 i = 12% Future Value - Single Cash Flow 1,254.40 1,404.93 1,573.52 1,762.34 2 3 4 5 Future Value - Single Cash Flow FVIF 12%,5 = (1.12) 5 = 1.76234 FV 5 = ($1,000)(1.76234) FV 5 = $1,762.34
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OEM 2009 Program Time Value of Money Page 2 Interest on Interest 0 $1,000.00 --- --- 1 $1,120.00 $120.00 --- Year Future Value Interest Interest on 2 $1,254.40 $254.40 $14.40 3 $1,404.93 $404.93 $30.53 4 $1,573.52 $573.52 $48.59 5 $1,762.34 $762.34 $68.82 i = 12% $162.34 ± Set payments to 1 per year (1 period) ± Clear All 1 ± P/YR 1 Calculation Using the 10B Now : N = number of periods (can be years) I/YR = interest rate per period Inputs 5 12 -1,000 0 N I/YR PV PMT FV Calculation Using the 10B ± Clear All Outputs 1,762.34 One of the cash flows (either input or output) will be negative. In this example we are depositing money (a negative or outflow) versus the ending value when we would get cash back (a positive or inflow). Period (n) 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 1.0000 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 1.1100 1.1200 1.1300 1.1400 1.1500 2 1.0000 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 1.2321 1.2544 1.2769 1.2996 1.3225 3 1.0000 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.3676 1.4049 1.4429 1.4815 1.5209 4 1.0000 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5181 1.5735 1.6305 1.6890 1.7490 5 1.0000 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.6851 1.7623 1.8424 1.9254 2.0114 6 1.0000 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.8704 1.9738 2.0820 2.1950 2.3131 7 1.0000 1.0721 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.0762 2.2107 2.3526 2.5023 2.6600 8 1.0000 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.3045 2.4760 2.6584 2.8526 3.0590 9 1.0000 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.5580 2.7731 3.0040 3.2519 3.5179 10 1.0000 1.1046 1.2190 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 2.8394 3.1058 3.3946 3.7072 4.0456 11 1.0000 1.1157 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.1518 3.4785 3.8359 4.2262 4.6524 Future Value Interest Factors of Single or Lump Sum Values: FVIFi,N = (1+i) n 12 1.0000 1.1268 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.4985 3.8960 4.3345 4.8179 5.3503 13 1.0000 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 3.8833 4.3635 4.8980 5.4924 6.1528 14 1.0000 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.3104 4.8871 5.5348 6.2613 7.0757 15 1.0000 1.1610 1.3459 1.5580 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 4.7846 5.4736 6.2543 7.1379 8.1371 16 1.0000 1.1726 1.3728 1.6047 1.8730 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950 5.3109 6.1304 7.0673 8.1372 9.3576 17 1.0000 1.1843 1.4002 1.6528 1.9479 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545 5.8951 6.8660 7.9861 9.2765 10.7613 18 1.0000 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599 6.5436 7.6900 9.0243 10.5752 12.3755 19 1.0000 1.2081 1.4568 1.7535 2.1068 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159 7.2633 8.6128 10.1974 12.0557 14.2318 20 1.0000 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 8.0623 9.6463 11.5231 13.7435 16.3665 21 1.0000 1.2324 1.5157 1.8603 2.2788 2.7860 3.3996 4.1406 5.0338 6.1088 7.4002 8.9492 10.8038 13.0211 15.6676 18.8215 22 1.0000 1.2447 1.5460 1.9161 2.3699 2.9253 3.6035 4.4304 5.4365 6.6586 8.1403 9.9336 12.1003 14.7138 17.8610 21.6447 23 1.0000 1.2572 1.5769 1.9736 2.4647 3.0715 3.8197 4.7405 5.8715 7.2579 8.9543 11.0263 13.5523 16.6266 20.3616 24.8915 24 1.0000 1.2697 1.6084 2.0328 2.5633 3.2251 4.0489 5.0724 6.3412 7.9111 9.8497 12.2392 15.1786 18.7881 23.2122 28.6252 25 1.0000 1.2824 1.6406 2.0938 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 10.8347 13.5855 17.0001 21.2305 26.4619 32.9190 $4.00 $5.00 F u t u r 15% Future Value of One Dollar $0.00 $1.00 $2.00 $3.00 01234567891 0 Number of Compounding Periods e V a l u e 0% 5% 10% Present Value - Single Cash Flow PV N = [FV] PV = [FV] [PVIF 1 (1+i) N _______ N = [FV] [PVIF i,N ] PVIF i,N = 1 (1+i) N _______
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OEM 2009 Program Time Value of Money Page 3 1,000.00 892.86 Value at t = 5 i = 12% 4 Present Value - Single Cash Flow 797.19 711.78 635.52 567.43 3 2 1 0 Present Value - Single Cash Flow PVIF 12%,5 = = 0.56743 PV = ($1 000)(0 56743 1 (1.12) 5 _________ 5 = ($1,000)(0.56743) PV 5 = $567.43 Inputs 5 12 0 -1,000 N I/YR PV PMT FV Calculation Using the 10B ± Clear All Outputs 567.43 Period (n) 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 1.0000 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 2 1.0000 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 3 1.0000 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.6750 0.6575 4 1.0000 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5718 5 1.0000 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 6 1.0000 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 7 1.0000 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759 8 1.0000 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 9 1.0000 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 10 1.0000 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472 11 1.0000 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875
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Chapter02TimeValueofMoney - OEM 2009 Program Time Value of...

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